A Note on L-double Gradation Fuzzy Topological and L-double Fuzzy Closure Spaces

We prove the existence of both final L-double gradation fuzzy topological spaces and final L-double fuzzy closure spaces. From this fact,we define and study the notions of the L-double quotient spaces and the sum of L-double fuzzy closure spaces. Finally,we study the additivity of two kinds of L-double fuzzy closure spaces.

ON BEST SIMULTANEOUS APPROXIMATION IN QUOTIENT SPACES

We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M and the quotient space W/M.

The Spectrum of Linear Operators on Quotient Indecomposable Banach Spaces

This paper discusses the special properties of the spectrum of linear operators （in particular, bounded linear operators） on quotient indecomposable Banach spaces; shows that in such spaces generators of C0-groups are always bounded linear operators, and that generators of C0-semigroups satisfy the spectral mapping theorem; and gives an example to show that the generators of C0-semigroups in quotient indecomposable spaces are not necessarily bounded.

Quotient space model based on algebraic structure

In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure is assumed as an algebra instead of a topology.As to obtain the algebraic quotient operator,the granulation must be uniquely determined by a congruence relation,and all the congruence relations form a complete semi-order lattice,which is the theoretical basis of granularities ' completeness.When the given equivalence relation is not a congruence relation,it defines the concepts of upper quotient and lower quotient,and discusses some of their properties which demonstrate that falsity preserving principle and truth preserving principle are still valid.Finally,it presents the algorithms and example of upper quotient and lower quotient.The work extends the quotient space theory from structure,and provides theoretical basis for the combination of the quotient space theory and the algebra theory.

Study on Logical Relations amongUnderground Survey Objects Using Quotient Topological Space

A soitable data model and data structure make underground survey objects maintained and operated easier. This paper gives a formal definition for underground survey objects. By making use of the quotient topological space, the author studies the logical relations among underground survey objects, a partiallyordered space uuder some conditions. An example is given to show the data model’s possible applications.

The Sequence-covering Compact Images of Paracompact Locally Compact Spaces

This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally compact metric spaces.

The rough representation and measurement of quotient structure in algebraic quotient space model

Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an equivalence relation. In this paper,definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure. Then the accuracy and roughness were defined to measure the quotient structure in quantification. Finally,a numerical example was given to demonstrate that the rough representation and measuring methods are efficient and applicable. The work has greatly enriched the algebraic quotient space model and granular computing theory.

QUOTIENT SPACE OF LMC-COMPACTIFICATION AS A SPACE OF z-FILTERS

The left multiplicative continuous compactification is the universal semigroup compactification of a semitopological semigroup.In this paper an internal construction of a quotient space of the left multiplicative continuous compactification of a semitopological semigroup is constructed as a space of z-filters

Several rough set models in quotient space

In order to deal with coarse-grained and multi-grained calculation problems,as well as granularity transformation problems in information system,quotient space theory is introduced in rough set theory.The main idea of this research is to try to maintain the important properties of the original space into the quotient space.Aimed to preserve the micro properties and the macro properties,two pairs of approximation operators on the quotient space are defined.When it comes to the composite of quotient spaces,the idea of these operators shows greater advantages.Examples are cited to illustrate possible applications of these operators,and their matrix representations are also given to make the calculations easy.Finally,all approximation operators on the quotient space involved so far are compared and their relationships are shown through a diagram.

The application of fuzzy equivalence relation based on the quotient space in cluster analysis

A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidimensional samples. Secondly, the fuzzy compatibility relation matrix of the model is converted into fuzzy equivalence relation matrix. Finally, the diagram of clustering genealogy is generated according to the fuzzy equivalence relation matrix, which enables the dynamic selection of different thresholds to effectively solve the problem of cluster analysis of the samples with multi-dimensional attributes.

A NOTE ON THE IMAGES OF M_1-SPACES

In this note,we give some conditions concerning that the countably bi-quotient closed mappings, and the closed mappings with each fiber having a σ-closure preserving outer base, preserve M1-spaces.

一种多粒度空间的快速构建方法

粒计算是模拟人脑多粒度认知模式处理复杂问题的一种方法.模糊商空间理论作为粒计算的一种典型模型,将复杂问题渐进式粒化成为分层递阶的多粒度空间,从而实现层次化的求解.然而,面对海量高维数据,现有模糊商空间模型通过模糊相似关系构建多粒度空间的效率将大幅降低.一方面,模糊相似关系需要计算数据空间中任意两个对象之间的相似性,不利于处理体量大的数据集;另一方面,模糊相似关系包含大量冗余信息,导致后续步骤中存在大量的冗余计算.因此,本文基于2近邻模糊关系,提出了多粒度空间的快速构建方法,在保证面向下游分类任务时性能不下降的前提下,极大地提升了多粒度空间构建效率.首先,基于k近邻算法提出k近邻模糊关系,并分析证明其关键性质;然后,面向多粒度空间构建任务,对k近邻模糊关系进行参数分析,从理论上证明k取2时即可包含数据空间中全部有效信息;随后,定义了最近邻和次近邻两阶段的有效位置数,提出了模糊相似关系有效值和有效位置提取算法,多粒度空间构建效率提升了75%左右.最后,通过在9个UCI数据集、3个UKB数据集、3个图像数据集和3个文本数据集上的相关实验,验证了该算法构建多粒度空间的高效性、正确性以及面向下游分类任务的有效性、稳定性和显著性.

基于代数粒的聚类方法

聚类,是机器学习的主要任务之一,也是粒计算理论的核心任务,即信息粒化。目前,基于粒计算的聚类算法中,大多数只基于粒属性进行聚类,而没有考虑粒结构,尤其是在代数结构应用广泛的信息领域。从粒计算的角度,提出一种基于代数粒的聚类方法。基于二元代数运算定义代数粒;提出一种基于代数粒的聚类方法,通过粒集的同余划分和粒结构的同态映射进行粒度聚类;将提出的聚类方法与容差邻域模型和商空间模型进行对比分析。结果表明,该新型方法具有更好的结构完备性和应用鲁棒性。基于代数粒的聚类方法从结构上丰富和扩展了粒度计算理论,为粒计算与机器学习的融合研究提供了理论依据。

生活圈视阈下公园绿地圈层分布及其协同区位演变特征——以南京为例

公园绿地是城市的民生性生态福祉,揭示其时空分布规律是提升生活圈生态宜居质量的关键。基于生活圈全服务设施要素体系,利用POI与土地利用数据,借助多环缓冲区与协同区位商方法,系统揭示2012、2016、2020年南京中心城区公园绿地布局特征与水平。结果表明:1)公园绿地集聚性与临近性在古城>副城>主城边缘,圈层特征显著;2)公园绿地在各级生活圈分布由均衡渐趋聚集,5 min生活圈是游园、社区公园的核心聚集区,大型公园绿地则多圈层均衡分布;3)公园绿地协同区位水平快速、均衡提升,其中游园与生活配套设施协同区位特征近似,社区公园与大型公园绿地协同区位水平仍较低。提出通过复合增效与跨区延伸、挖潜拓维与内外联动、多功能补位与缩距提质,满足不同区域居民日常性、偶发性活动需求。成果深化了生活圈中公园绿地布局演化规律,可为协同配置公园绿地与服务设施要素提供科学依据。

杭州主城区中西快餐连锁店区位选择空间关联特征

借助杭州快餐连锁店区位等POI数据,运用核密度、协同区位商方法和地理加权回归模型,分析杭州主城区中西快餐连锁店区位选择的空间关联特征,结果表明:(1)杭州主城区中西快餐连锁店空间热点在中心城区集中分布,并呈星射状向外扩散,中西快餐连锁店的空间分布联系密切.(2)中西快餐连锁店空间分布之间存在一定协同关联性,中式快餐连锁店邻近西式快餐连锁店布局的倾向更强,且运营模式相近的中西快餐连锁店品牌之间的协同区位商也越大.(3)中西快餐连锁店空间关联区位呈现中心集聚、线状延伸特征,且中式快餐连锁店与西式快餐连锁店关联的局域关联空间分布更为显著.(4)中西快餐连锁店空间分布同时呈现相似性和分异性特征,西式快餐连锁店普遍邻近购物商场,而中式快餐连锁店除邻近购物商场之外,还存在部分区位更邻近产业园区、写字楼和居民区,并且西式快餐连锁店受不同区位因素影响的范围均大于中式快餐连锁店.

基于信息熵和差别矩阵的属性约简方法

针对无决策属性的信息系统,定义了无决策属性的差别矩阵,利用商空间理论下信息熵的计算方法,提出了一种“空不变”无决策属性约简方法。该方法从属性约简的本质出发,将属性造成等价类发生改变的可能性数值化,进而实现属性约简。通过实例验证了方法的有效性,并通过与已有方法的对比和实验结果分析,进一步证实了该方法能更准确地识别出关键属性,完成属性约简。

SOME RESULTS RELATED TO THE SEPARABLE QUOTIENT PROBLEM

The problem whether every infinite dimensional Banach space has an infinite dimensional separable quotient space has remained unsolved for a long time. In this paper we prove: the Banach space X has an infinite dimensional separable quotient if and only if X has an infinite dimensional separable quasicomplemented subspace, also if and only if there exists a Banach space Y and a bounded linear operator T is an element of B(Y,X such that the range of T is nonclosed and dense in X. Besides, the other relevant questions for such spaces e.g. the question on operator ideals that on H.I.(hereditarily indecomposable) spaces, that on invariant subspaces of operators, etc, are also discussed.

A note on equicontinuous maps of graph space

Let G be a graph and f: G→ G be a continuous map with at least one periodic point. Using the quote space method, the paper addresses that f is an equicontinuous map if and only if one of the following End(G)+2k+1 conditions holds: 1) {f jm(End(G)+2k)!}∞j=1 is uniformly convergent, in which m=1,2,…, End(G)+2k; and 2) There is a positive integer n esuring that {f jn}∞j=1 is uniformly convergent.

学习空间支持下的学习范式转型:建立主体责任

对于学习目标及其价值理解的一致性,是实现高质量教育目标的基础。学习个体的个人特质与认知习惯等方面存在的差异,容易导致理解的不一致性,并通过学习的结果商数体现出来。从学习的视角理解数字化转型,就是要构建有利于促进个体发挥主体性的学习生态,建立具有相同学习价值追求的共同体,以高品质发展作为共同理想,建立相互信任与尊重,推动个体形成主体责任。学习空间设计需要尊重学习个体的身体、生理与心理等特质,具备调整功能,让学习个体能够具身参与学习、具生参与学习、具心参与学习,推动学习从形式向范式转型。范式的形成是因为实践中出现了新的问题,并且范式具有一定的共性特征。实践的条件发生了变化,范式就可能会转型。学习范式的转型依赖于研究与实践领域形成关于学习的共同认识,并有助于促进认识的发生,但外部支持条件的变化才可以让转型的理念转化为实践。重构的新型学习范式,应当能够唤醒学习个体的主体意识,主动发挥学习的主体决策责任。

一种商空间理论下信息熵的属性权重确定方法

在对多属性多目标方案进行排序或决策时,属性权重的确定对最终决策结果的影响非常重要。针对无决策属性的多样本数据,提出了一种基于层次商空间信息熵的属性计算方法。该方法通过对样本数据的相似度和等价关系矩阵分层建立商空间结构,重新定义商空间理论下的信息熵,在商集上计算确定属性权重。最后将该方法应用到一个既无决策属性又无核属性的油田开发多目标决策数据集中,验证了该方法的科学性和可行性。